The respective functions f(x) obtained from the given derivatives and points are
35. f(x) = 2x² + x - 1.
36. f(x) = 3x - x² - 1.
37. f(x) = -x²/2 - x³/3 + 9/2.
38. f(x) = x³ + 3x² - 2x + 6.
39. f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.
40. f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.
41. f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.
42. f(x) = 3ln|x| - 4x + 4.
To find the function f(x) based on the given derivative f'(x) and a particular point (a, b), we can integrate f'(x) with respect to x and then use the given point to determine the constant of integration.
Let's go through each exercise:
35. f'(x) = 4x + 1; (1, 2)
Integrating f'(x) gives:
f(x) = 2x² + x + C
Using the given point (1, 2), we can substitute x = 1 and y = 2 into the equation:
2 = 2(1)² + 1 + C
2 = 2 + 1 + C
C = -1
Therefore, f(x) = 2x² + x - 1.
36. f'(x) = 3 - 2x; (0, -1)
Integrating f'(x) gives:
f(x) = 3x - x² + C
Using the given point (0, -1), we can substitute x = 0 and y = -1 into the equation:
-1 = 0 + 0 + C
C = -1
Therefore, f(x) = 3x - x² - 1.
37. f'(x) = -x(x + 1); (-1, 5)
Integrating f'(x) gives:
f(x) = -x²/2 - x³/3 + C
Using the given point (-1, 5), we can substitute x = -1 and y = 5 into the equation:
5 = -(-1)²/2 - (-1)³/3 + C
5 = -1/2 + 1/3 + C
C = 27/6 = 9/2
Therefore, f(x) = -x²/2 - x³/3 + 9/2.
38. f'(x) = 3x² + 6x - 2; (0, 6)
Integrating f'(x) gives:
f(x) = x³ + 3x² - 2x + C
Using the given point (0, 6), we can substitute x = 0 and y = 6 into the equation:
6 = 0 + 0 - 0 + C
C = 6
Therefore, f(x) = x³ + 3x² - 2x + 6.
39. f'(x) = x³ - 2/x² + 2; (1, 3)
Integrating f'(x) gives:
f(x) = (1/4)x⁴ + 2/x + 2x + C
Using the given point (1, 3), we can substitute x = 1 and y = 3 into the equation:
3 = (1/4)(1)⁴ + 2/1 + 2(1) + C
3 = 1/4 + 2 + 2 + C
C = -19/4
Therefore, f(x) = (1/4)x⁴ + 2/x + 2x - 19/4.
40. f'(x) = x⁽⁻¹/²⁾ + x; (1, 2)
Integrating f'(x) gives:
f(x) = 2x⁽¹/²⁾ + (1/2)x² + C
Using the given point (1, 2), we can substitute x = 1 and
y = 2 into the equation:
2 = 2(1)⁽¹/²⁾ + (1/2)(1)² + C
2 = 2 + 1/2 + C
C = 1/2
Therefore, f(x) = 2x⁽¹/²⁾ + (1/2)x² + 1/2.
41. f'(x) = e⁽⁻ˣ⁾ + x; (0, 4)
Integrating f'(x) gives:
f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + C
Using the given point (0, 4), we can substitute x = 0 and y = 4 into the equation:
4 = -e⁽⁻⁰⁾+ (1/2)(0)² + C
4 = -1 + 0 + C
C = 5
Therefore, f(x) = -e⁽⁻ˣ⁾ + (1/2)x² + 5.
42. f'(x) = 3/x - 4; (1, 0)
Integrating f'(x) gives:
f(x) = 3ln|x| - 4x + C
Using the given point (1, 0), we can substitute x = 1 and y = 0 into the equation:
0 = 3ln|1| - 4(1) + C
0 = 0 - 4 + C
C = 4
Therefore, f(x) = 3ln|x| - 4x + 4.
These are the respective functions f(x) obtained from the given derivatives and points.
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A concrete slab has the dimensions 4 yd by 2 yd by 1.2 yd. What is the volume of 40 of these concrete slabs
The volume of 40 of the concrete slabs given the dimensions of one concrete slab is 384 yd³.
What is the volume of one concrete slab?The concrete slab has the shape of a rectangular prism. So, the volume of a rectangular prism would be used to determine the volume of the concrete slabs.
Volume of one concrete slab = length x width x height
4 x 2 x 1.2 = 9.6 yd³
Volume of 40 concrete slabs = 40 x 9.6 = 384 yd³
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Which measurements are less than 475 inches?
x-4.88=-5.78
solve for x
Answer:
-0.9
Step-by-step explanation:
Answer:
x =-.9
Step-by-step explanation:
x-4.88=-5.78
Add 4.88 to each side
x-4.88+4.88=-5.78+4.88
x =-.9
wildlife biologists believe that the weights of adult trout can be described by a normal model with a standard deviation of 1.2 pounds. if only 7% of adult trout weigh more than 5 pounds what is the mean weight (in pounds) of adult trout?
The mean weight of adult trout is 3.224 pounds is the answer.
Given, A normal model is used to describe the weights of adult trout, with a standard deviation of 1.2 pounds. It is known that only 7% of adult trout weigh more than 5 pounds.
To calculate the mean weight (in pounds) of adult trout, the following steps need to be followed:
Step 1: Find the z-score for the given percentage value.
The z-score formula is given by: z = (x - μ) / σ where x is the value of the variable, μ is the mean, and σ is the standard deviation.
Step 2: Once we have the z-score, we can find the corresponding value of x using the z-score table.
We need to find the z-score corresponding to the 93rd percentile as only 7% of the trout weigh more than 5 pounds.z = (x - μ) / σ
For a one-tailed distribution with α = 0.07, the z-score is 1.48, approximately.
Therefore, we have1.48 = (5 - μ) / 1.2Multiplying both sides by 1.2, we get1.776 = 5 - μ
Subtracting 5 from both sides, we getμ = 5 - 1.776μ = 3.224
Therefore, the mean weight of adult trout is 3.224 pounds.
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Tema: valor numérico de expresiones algebraicas
A= 2
B= 1
X= 3
Y= 5
Z= -3
Answer:
1. 61
2. -8
3. 731
4. -16
5. -5
Step-by-step explanation:
Please help, i need it done by today,
Answer:
x= 28
do i have to explain
Step-by-step explanation:
Find the general solution to the homogeneous system of DE: -11 x' = Ax where A = [-26 41 Hint: Write your answer x(t) in the form of eat [cos(ht) + sin(bt)].
The general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
To find the general solution to the homogeneous system of differential equations -11x' = Ax, where A = [-26 4; 1 1], we first need to find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| -26-λ 4 |
| 1 1-λ |
Expanding the determinant, we have:
(-26-λ)(1-λ) - 4 = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -7
λ₂ = -20
Next, let's find the corresponding eigenvectors.
For λ₁ = -7:
(A + 7I)v₁ = 0
| -19 4 |
| 1 8 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 4 |
|-1 |
For λ₂ = -20:
(A + 20I)v₂ = 0
| -6 4 |
| 1 21 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 2 |
|-1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
Substituting the values of the eigenvalues and eigenvectors, we get:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
Simplifying this expression, we get:
x(t) = | 4c₁ * [tex]e^{(-7t)[/tex] + 2c₂ * [tex]e^{(-20t)[/tex] |
|-c₁ * [tex]e^{(-7t)[/tex] - c₂ * [tex]e^{(-20t)[/tex]) |
Therefore, the general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
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Angle 5 Has what angle
A.alternate interior angle
B.alternate exterior angle
C.same side interior angle
Which null distribution is used for a hypothesis test of a single population proportion? Select one: O a. t-distribution with df = n - 1 O b. standard normal distribution O c. t-distribution with df = n1 + n2 – 2
The null distribution used for a hypothesis test of a single population proportion is the standard normal distribution. The correct answer is b).
When conducting a hypothesis test for a single population proportion, we use the standard normal distribution as the null distribution. This is based on the assumption that the sampling distribution of the sample proportion follows a normal distribution when the sample size is sufficiently large.
The hypothesis test for a single population proportion involves comparing the observed sample proportion to the hypothesized population proportion. We calculate the test statistic, which is the standard error of the sample proportion under the null hypothesis, divided by its standard deviation.
Since the test statistic follows a normal distribution under the null hypothesis, we compare it to critical values from the standard normal distribution to determine the p-value and make a decision regarding the null hypothesis.
Therefore, correct option is B.
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An analyst studied the average savings of recent college graduates. The results of the study reveal the following: n=40, sample mean = $16,000, sample standard deviation = $5,000. The probability that a randomly selected recent graduate has savings of $18,000 or more is closet to Hint: You need to calculate a z-score and remember to use the standard error in your calculations more than 5% less than 1% about 95% about 68%.
If The results of the study reveal that n=40, sample mean = $16,000, and sample standard deviation = $5,000 then the probability is about 65.54%.
To calculate the probability that a randomly selected recent graduate has savings of $18,000 or more, we first need to calculate the z-score using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, x = $18,000, μ = $16,000, and σ = $5,000.
Substituting these values into the formula, we get z = (18,000 - 16,000) / 5,000 = 0.4.
Next, we can use a z-table or calculator to find the corresponding probability.
Looking up the z-score of 0.4 in the z-table, we find that the probability is approximately 0.6554, or about 65.54%.
Therefore, the probability that a randomly selected recent graduate has savings of $18,000 or more is approximately 65.54%.
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According to the central limit theorem, which of the following statements is true?
a. The distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.
b. The center of a distribution is limited to move no more than 1.5 standard deviations (also known as the 1.5 sigma shift).
c. The center of dispersion of a sample (
) is limited by the size of the sample.
d. The central tendency of a distribution is limited by common-cause variation.
The central limit theorem,option (A) is correct
According to the central limit theorem, the following statement is correct:
a. Regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independent variables with identical distributions will be approximately normal.
Regardless of the original distribution's shape, the central limit theorem states that independent and identically distributed variables tend to approximate a normal distribution when added together or averaged. We are able to draw conclusions about the parameters of the population based on the statistics of the sample because this is one of the fundamental principles of statistical inference.
The central limit theorem is unrelated to the other statements (b, c, and d). Statements b, c, and d all refer to common-cause variation rather than the central limit theorem, while statement d does not accurately describe the central limit theorem.
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True or false: On average, eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study.
The statement that eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. This statement is true.
In order to better understand what eta-squared, partial eta-squared, and R-squared are, we must first understand what the proportion of variance explained is. The proportion of variance explained refers to the amount of variation in one variable that is accounted for by another variable or variables. All three of these measures are measures of effect size, which means they are used to determine the strength of the relationship between two variables. They also all refer to the proportion of variance explained within a study. However, they differ in terms of how much variance they account for. Eta-squared is a measure of effect size that is used in ANOVA to determine the proportion of variance in the dependent variable that is accounted for by the independent variable. Partial eta-squared, on the other hand, is used to determine the proportion of variance that is accounted for by the independent variable when controlling for other variables.
Finally, R-squared is a measure of effect size that is used in regression analysis to determine the proportion of variance in the dependent variable that is accounted for by the independent variable.
In conclusion, all three of these measures of effect size are used to determine the proportion of variance explained within a study.
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Find the parametric equations for the circle with radius 4 and centered at (-3,4) circle traced clockwise starting at (-3,0). include the domain.
The parametric equations for the circle with radius 4 and centered at (-3,4), traced clockwise starting at (-3,0), are x = -3 + 4cos(t) and y = 4 + 4sin(t), where t is the parameter representing the angle of rotation. The domain for these equations is 0 ≤ t ≤ 2π.
To obtain the parametric equations for the circle, we start by considering the general equation of a circle centered at (h,k) with radius r:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
In this case, the circle is centered at (-3,4) and has a radius of 4, so the equation becomes:
[tex](x + 3)^2 + (y - 4)^2 = 16[/tex]
To represent the circle parametrically, we can use the trigonometric functions cosine and sine to describe the x and y coordinates, respectively. We can rewrite the equation as:
(x + 3) = 4cos(t)
(y - 4) = 4sin(t)
Simplifying, we obtain:
x = -3 + 4cos(t)
y = 4 + 4sin(t)
These equations describe the x and y coordinates of points on the circle as a function of the angle t. The parameter t represents the angle of rotation around the circle. To trace the circle clockwise, we need to assign decreasing values to t. The domain for t is 0 ≤ t ≤ 2π, which corresponds to a full revolution around the circle.
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Mr. White is renting an oversized truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 325+100d to find how much he will pay for a 13-day rental. Each day = $100
Answer:
$1,625
Step-by-step explanation:
Given:
Total cost = 325 + 100d
Where,
325 = fixed cost
100 = cost per day
d = number of days
Find the total cost when d = 13 days
Total cost = 325 + 100d
= 325 + 100d
= 325 + 100(13)
= 325 + 1,300
= 1,625
Total cost = $1,625
Jasmine bought four potted plants. Two of the plants cost $6.65, and the others cost $4 and $7.15. How much money did jasmine spend in all?
Answer:
$24.45
Step-by-step explanation:
6.65 + 4 + 7.15 + 6.65 = 24.45
Can someone plzzz helppp meee!!!
Answer:
Step-by-step explanation:
Solve the following recurrence relations (a) [6pts] an = 3an-2, Q1 = 1, 42 = 2. b) [6pts] an = an-1 + 2n – 1,01 = 1, using induction (Hint: compute the first few terms, = pattern, then verify it).
a) an = 3(n-2) if n is even and an = 3(n-3) if n is odd
b) It is proved that an = n².
a)Given recurrence relation is an = 3an-2, Q1 = 1, Q2 = 2.
We have to find an in terms of n.
Step 1: Finding the pattern
Let us find the values of a1, a2, a3 and a4 a1 = Q1 = 1, a2 = Q2 = 2, a3 = 3, a1 = 3, a4 = 3a2 = 3 x 2 = 6
Let us represent it as a table
Step 2: Writing the general expression
The sequence obtained is an = 1, 2, 6, 18, 54, …We can see that an = 3an-2
If n is even, then an = 3(n-2)
If n is odd, then an = 3(n-3)
Step 3: Writing the final expression
The general expression of an is as follows:
an = 3(n-2) if n is even and an = 3(n-3) if n is odd
b) Given recurrence relation is an = an-1 + 2n – 1, a1 = 1, using induction
Let us prove that an = n² by induction
Step 1: Verification of base case
When n = 1an = a1 = 1
We have to prove that a1 = 12 an = n2 = 1
Therefore, the base case is verified.
Step 2: Let us assume that an = n2 is true for some k such that k > 0i.e., ak = k² (Inductive Hypothesis)
Step 3: Let us verify that an = n2 is true for n = k+1i.e., prove that ak+1 = (k+1)²
Using the recurrence relation given, we haveak+1 = ak + 2k+1 – 1 = k2 + 2k + 1 = (k+1)²
Therefore, the proof is complete. It is proved that an = n².
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These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
5 cm
Surface Area = [? ] cm2 Surface Area = 111 cm?
9514 1404 393
Answer:
17.8 cm²
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of the linear dimensions. The small/large linear dimension ratio is 2/5, so the surface area of the smaller cone is ...
A = (2/5)²(111 cm²) = 17.76 cm²
The area of the smaller cone is about 17.8 cm².
Answer: [tex]17.8 cm^{2}[/tex]
Write the following permutation as a product of disjoint cycles and thereafter as a product of transpositions 1 2 3 4 5 6 7 8 8 2 6 3 7 4 5 1 (62848X)
The given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).
To express the given permutation (62848X) as a product of disjoint cycles, we start by examining each element and its corresponding image under the permutation.
1 maps to 6.
6 maps to 2.
2 maps to 8.
8 maps to 4.
4 maps to 8 (since X represents a fixed point, meaning it remains unchanged).
Now, let's write these mappings as disjoint cycles:
(1 6 2 8 4)
The cycle notation indicates that 1 maps to 6, 6 maps to 2, 2 maps to 8, 8 maps to 4, and 4 maps back to 1.
Next, we'll express this permutation as a product of transpositions. A transposition swaps two elements.
We can achieve this by breaking down the cycle (1 6 2 8 4) into transpositions:
(1 6)(6 2)(2 8)(8 4)
Each pair of adjacent elements within the cycle forms a transposition. For example, (1 6) represents the transposition that swaps 1 and 6, (6 2) swaps 6 and 2, and so on.
Thus, the given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).
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Can someone please help
okay sorry
Step-by-step explanation:
i just wanted point
Rico and Darla each measured a side and height on the triangle below to find its area.
Rico’s side measured 7.5 m and Darla’s side measured 9 m.
Choose True or False for each statement.
A triangle with two base and side length measurements. One side length is nine meters, and the height from that side is five meters. The other side length is seven and five-tenths meters and the height from that side is six meters.
Darla can use either the height of 6 meters or the height of 5 meters to find the area of the triangle.
Choose...
If Darla uses the height of 6 meters and Rico uses the height of 5 meters, they will find the same area of the triangle.
Choose...
If Rico uses the height of 6 meters and Darla uses the height of 5 meters, they will find the same area of the triangle.
Choose...
The area of the triangle is 22.5 square meters.
Choose...
Answer: not sure
Step-by-step explanation:
Write an equation in point slope form that is parallel to AB with endpoints A (2, -1) and B (4, 5) that goes through the point (1.5, 4)
Answer:
[tex]y = 3x - 0.5[/tex]
Step-by-step explanation:
Given
Goes through
[tex]C = (1.5,4)[/tex]
Parallel to AB
[tex]A = (2,-1)[/tex]
[tex]B = (4,5)[/tex]
Required
Determine the line equation
First, calculate the slope of AB
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5--1}{4-2}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m = 3[/tex]
The line is said to be parallel to AB. This implies that their slopes are equal.
The equation of the line is then calculated as:
[tex]y = m(x - x_1) + y_2[/tex]
Where:
[tex](x_1,y_1) = (1.5,4)[/tex]
So:
[tex]y = 3*(x - 1.5) + 4[/tex]
[tex]y = 3x - 4.5 + 4[/tex]
[tex]y = 3x - 0.5[/tex]
the area is ___ square units
Answer:
12 units²
Step-by-step explanation:
The height is 2, and the width is 12.
Now multiply and that gives us 24. But that's not the full answer.
Since a triangle's area is half of a square, we divide by 2, leaving us with 12. (plus the label which is units²)
what is the value of x ?
Step-by-step explanation:
The line JK is tangent to the circle h so <KJH is a right angle.
[tex]a^2+b^2=c^2[/tex]
[tex]15^2+20^2=x^2[/tex]
[tex]625=x^2\\x=25[/tex]
Hope that helps :)
Figure 222 is a scaled copy of Figure 111.
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Answer:
if im corect the anwser is 3.14 (Side note) this is the wrong question i was anwsering to
State the name of the property illustrated. 2 + (6 + 4) = (2 + 16 + 74 () A Associative O Distributive Commutative o Both associative and commutative
The property which is represented in the equation : "2 + (√6 + √4) = (2 + √6) + √4" is (a) Associative.
The "Associative-Property" is a fundamental property of addition that states that the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, the way they are grouped does not change the result.
In the given equation : 2 + (√6 + √4) = (2 + √6) + √4, we see that the numbers (√6 + √4) and (2 + √6) are grouped differently, but the sum remains the same. This is because the associative property , which allows us to rearrange the brackets and change the grouping without affecting the final result.
Therefore, the correct option is (a).
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The given question is incomplete, the complete question is
State the name of the property illustrated : 2 + (√6 + √4) = (2 + √6) + √4
(a) Associative
(b) Distributive
(c) Commutative
(d) Both associative and commutative.
Can someone help me with this. Will Mark brainliest.
Answer:
the distance between the two points is √130.
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 = 9^2 = 81
b^2 = 7^2 = 49
c^2 = 81 + 49 = 130
c = √130
PLEASE HELP FAST I WIL MARK BRAINLIEST
Answer: AB = 15 because sides AB and AD are congruent
Step-by-step explanation:
A sphere has a radius of 9 feet. A second sphere has a radius of 6 feet. What is the difference of the volumes of the spheres? The volume of the larger sphere is π cubic feet greater than the volume of the smaller sphere.
Answer:
684 π
Step-by-step explanation:
volume of a sphere = (4/3) x (n) x (r^3)
n = 22/7
r = radius
volume of larger sphere
4/3 x n x 9³ = 972 n
4/3 x n x 6³ =288n
972n - 288n = 684n
i just don’t understand
Answer:
the answer is 9
Step-by-step explanation: